How can I come to know how a catalyst affects a reaction when the reaction and the catalyst used is known.
I searched the internet for an answer but could not find one.
Empirically, you dump the catalyst to be tested into the reaction and determine the rate with/without for various catalytic loadings. This will tell you whether it increases or decreases the rate of the reaction.
Assuming that you are vaguely asking about a specific reaction and catalyst, you aren't going to get a specific answer without specifically mentioning them in your question. (I think that was enough specificity for now!).
More generally, you will probably want to search for university level teaching resources on transition metal or biological catalysts wherein you might find your answer. Higher level reading would be to use something like Web of Knowledge or Reaxys to find publications on your catalyst/reaction of question.
There is no simple way to know it. The mechanism in some of the cases of catalysis is known, therefore some predictions can be made. Also there are many cases where the given catalytic reaction has a great practical significance, therefore it is thoughtlessly tested with different combinations of reagents, and the results are published.
At a basic level, a catalyst lowers the activation energy of a reaction, which makes it easier for the reaction to occur ("speeding it up"). The catalyst is not chemically consumed by the process. (Though corrosion, coking, and other side reactions can still deteriorate catalyst perofmance)
Further details depend on the specific reaction and catalyst.
Here is an example by which one can I come to understand how a catalyst affects a reaction given that the net reaction and the catalyst are known. Lets look at the summary net Haber–Weiss reaction in which iron ions under acidic conditions are said to be the catalytic:
.O2− + H2O2 ---H+,Fe(II),Fe(III)→ .OH + O2 + OH- [R3]
The reaction steps are believed to proceed in the presence of iron ions (and more so also in the presence of Cu(II) forming a redox couple equilibrium, Cu(II) + Fe(II) = Cu(I) + Fe(III)):
Fe(III) + .O2- (+ H+ ) = Fe(II) + O2 (+ H+ ) [R1]
where Reaction R1 is the reverse of the oxidation of ferrous to ferric in the presence of acid and oxygen witnessed in a spontaneous electrochemical based corrosion of iron to rust which proceeds as follows:
Fe → Fe(II) + 2 e-
O2 + e- → .O2-
Fe(II) = Fe(III) + e-
where the net of the last two spontaneous electrochemical half cell reactions is:
O2 + Fe(II) = .O2- + Fe(III)
which is the reverse of Reaction R1, with the implication being that R1 is the slow backward (or reverse) reaction. Next is the well known Fenton reaction:
Fe(II) + H2O2 → Fe(III) + .OH + OH− [R2]
where the net of R1 and R2 produces R3. The role of the iron ions catalyst in acidic conditions (and copper ions assisting in its recycling) is apparent as is also why R3 (per R1) is an observed slow reaction. The presence of H+ would remove OH- and be catalytic for R2. The addition of some NaCl, which I would argue serves as an electrolyte for the electrochemical aspects of the system, apparently accelerates the reaction rate, although researchers give other arguments.